P-NDOP and P-decompositions of $ℵ_{ϵ}$-saturated models of superstable theories

Saharon Shelah; Michael C. Laskowski

Displaying similar documents to “P-NDOP and P-decompositions of $ℵ_{ϵ}$ -saturated models of superstable theories”

Existentially closed II₁ factors

Ilijas Farah, Isaac Goldbring, Bradd Hart, David Sherman (2016)

Fundamenta Mathematicae

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We examine the properties of existentially closed ( $^{ω}$ -embeddable) II₁ factors. In particular, we use the fact that every automorphism of an existentially closed ( $^{ω}$ -embeddable) II₁ factor is approximately inner to prove that Th() is not model-complete. We also show that Th() is complete for both finite and infinite forcing and use the latter result to prove that there exist continuum many nonisomorphic existentially closed models of Th().

The decidability of some $ℵ_{0}$ -categorical theories

James H. Schmerl (1976)

Colloquium Mathematicae

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Infinitesimal CR automorphisms for a class of polynomial models

Martin Kolář, Francine Meylan (2017)

Archivum Mathematicum

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In this paper we study infinitesimal CR automorphisms of Levi degenerate hypersurfaces. We illustrate the recent general results of [18], [17], [15], on a class of concrete examples, polynomial models in $ℂ^{3}$ of the form $ℑ w = ℜ (P (z) \bar{Q (z)})$ , where $P$ and $Q$ are weighted homogeneous holomorphic polynomials in $z = (z_{1}, z_{2})$ . We classify such models according to their Lie algebra of infinitesimal CR automorphisms. We also give the first example of a non monomial model which admits a nonlinear rigid automorphism. ...

Constructibility in Ackermann's set theory

C. Alkor

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CONTENTSIntroduction......................... 5Section I. Preliminaries............ 6 § 1. Notation..................... 6 § 2. Ackermann’s set theory and some extensions................. 7 § 3. Absoluteness............................................... 8 § 4. Ordinals................................................... 9 § 5. Reflection principles...................................... 10Section 2. The usual notion of constructibility.............. 11 § 1. General considerations about...

Higher order spreading models

S. A. Argyros, V. Kanellopoulos, K. Tyros (2013)

Fundamenta Mathematicae

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We introduce higher order spreading models associated to a Banach space X. Their definition is based on ℱ-sequences ${(x_{s})}_{s \in ℱ}$ with ℱ a regular thin family and on plegma families. We show that the higher order spreading models of a Banach space X form an increasing transfinite hierarchy ${(ℳ_{ξ} (X))}_{ξ < ω ₁}$ . Each $ℳ_{ξ} (X)$ contains all spreading models generated by ℱ-sequences ${(x_{s})}_{s \in ℱ}$ with order of ℱ equal to ξ. We also study the fundamental properties of this hierarchy.

Counting models of set theory

Ali Enayat (2002)

Fundamenta Mathematicae

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Let T denote a completion of ZF. We are interested in the number μ(T) of isomorphism types of countable well-founded models of T. Given any countable order type τ, we are also interested in the number μ(T,τ) of isomorphism types of countable models of T whose ordinals have order type τ. We prove: (1) Suppose ZFC has an uncountable well-founded model and $κ \in ω \cup ℵ ₀, ℵ ₁, 2^{ℵ ₀}$ . There is some completion T of ZF such that μ(T) = κ. (2) If α <ω₁ and μ(T,α) > ℵ₀, then $μ (T, α) = 2^{ℵ ₀}$ . (3) If α < ω₁ and T ⊢ V ≠ OD,...

Completeness properties of classical theories of finite type and the normal form theorem

Peter Päppinghaus

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CONTENTSIntroduction........................................................................................................................................................................................................................50. Terminology and preliminaries......................................................................................................................................................................................121. The extent of cut elimination by...

The Gibbs phenomenon and Lebesgue constants for regular $A (λ)$ means

V. Swaminathan (1977)

Matematički Vesnik

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Coleman automorphisms of finite groups with a self-centralizing normal subgroup

Jinke Hai (2020)

Czechoslovak Mathematical Journal

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Let $G$ be a finite group with a normal subgroup $N$ such that $C_{G} (N) \leq N$ . It is shown that under some conditions, Coleman automorphisms of $G$ are inner. Interest in such automorphisms arose from the study of the normalizer problem for integral group rings.

The number of $L_{\infty κ}$ -equivalent nonisomorphic models for κ weakly compact

Saharon Shelah, Pauli Vaisanen (2002)

Fundamenta Mathematicae

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For a cardinal κ and a model M of cardinality κ let No(M) denote the number of nonisomorphic models of cardinality κ which are $L_{\infty, κ}$ -equivalent to M. We prove that for κ a weakly compact cardinal, the question of the possible values of No(M) for models M of cardinality κ is equivalent to the question of the possible numbers of equivalence classes of equivalence relations which are Σ¹₁-definable over $V_{κ}$ . By [SV] it is possible to have a generic extension where the possible numbers of equivalence...

Characterizing the powerset by a complete (Scott) sentence

Ioannis Souldatos (2013)

Fundamenta Mathematicae

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This paper is part II of a study on cardinals that are characterizable by a Scott sentence, continuing previous work of the author. A cardinal κ is characterized by a Scott sentence $ϕ_{ℳ}$ if $ϕ_{ℳ}$ has a model of size κ, but no model of size κ⁺. The main question in this paper is the following: Are the characterizable cardinals closed under the powerset operation? We prove that if $ℵ_{β}$ is characterized by a Scott sentence, then $2^{ℵ_{β + β ₁}}$ is (homogeneously) characterized by a Scott sentence, for all 0 <...

Twistor transforms of quaternionic functions and orthogonal complex structures

Graziano Gentili, Simon Salamon, Caterina Stoppato (2014)

Journal of the European Mathematical Society

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The theory of slice-regular functions of a quaternion variable is applied to the study of orthogonal complex structures on domains $Ω$ of $ℝ^{4}$ . When $Ω$ is a symmetric slice domain, the twistor transform of such a function is a holomorphic curve in the Klein quadric. The case in which $Ω$ is the complement of a parabola is studied in detail and described by a rational quartic surface in the twistor space $ℂ P^{3}$ .

Automorphisms of $(λ) / ℐ_{κ}$

Paul Larson, Paul McKenney (2016)

Fundamenta Mathematicae

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We study conditions on automorphisms of Boolean algebras of the form $(λ) / ℐ_{κ}$ (where λ is an uncountable cardinal and $ℐ_{κ}$ is the ideal of sets of cardinality less than κ ) which allow one to conclude that a given automorphism is trivial. We show (among other things) that every automorphism of $(2^{κ}) / ℐ_{κ ⁺}$ which is trivial on all sets of cardinality κ⁺ is trivial, and that $M A_{ℵ ₁}$ implies both that every automorphism of (ℝ)/Fin is trivial on a cocountable set and that every automorphism of (ℝ)/Ctble is trivial. ...

On cardinalities of algebras of formulas for $ω_{0}$ -categorical theories

Jan Waszkiewicz (1973)

Colloquium Mathematicae

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The group of automorphisms of $L_{\infty}$ is algebraically reflexive

Félix Cabello Sánchez (2004)

Studia Mathematica

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We study the reflexivity of the automorphism (and the isometry) group of the Banach algebras $L_{\infty} (μ)$ for various measures μ. We prove that if μ is a non-atomic σ-finite measure, then the automorphism group (or the isometry group) of $L_{\infty} (μ)$ is [algebraically] reflexive if and only if $L_{\infty} (μ)$ is *-isomorphic to $L_{\infty} [0, 1]$ . For purely atomic measures, we show that the group of automorphisms (or isometries) of $ℓ_{\infty} (Γ)$ is reflexive if and only if Γ has non-measurable cardinal. So, for most “practical” purposes, the automorphism...

On automorphisms of the Banach space $ℓ_{\infty} / c ₀$

Piotr Koszmider, Cristóbal Rodríguez-Porras (2016)

Fundamenta Mathematicae

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We investigate Banach space automorphisms $T : ℓ_{\infty} / c ₀ \to ℓ_{\infty} / c ₀$ focusing on the possibility of representing their fragments of the form $T_{B, A} : ℓ_{\infty} (A) / c ₀ (A) \to ℓ_{\infty} (B) / c ₀ (B)$ for A,B ⊆ ℕ infinite by means of linear operators from $ℓ_{\infty} (A)$ into $ℓ_{\infty} (B)$ , infinite A×B-matrices, continuous maps from B* = βB∖B into A*, or bijections from B to A. This leads to the analysis of general bounded linear operators on $ℓ_{\infty} / c ₀$ . We present many examples, introduce and investigate several classes of operators, for some of them we obtain satisfactory representations and for...

Assertion Q distinguishes topologically ω* and $𝔪$ when $𝔪$ regular and $𝔪 > ω$

R. Frankiewicz (1978)

Colloquium Mathematicae

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On the structure of the set of higher order spreading models

Bünyamin Sarı, Konstantinos Tyros (2014)

Studia Mathematica

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We generalize some results concerning the classical notion of a spreading model to spreading models of order ξ. Among other results, we prove that the set $S M_{ξ}^{w} (X)$ of ξ-order spreading models of a Banach space X generated by subordinated weakly null ℱ-sequences endowed with the pre-partial order of domination is a semilattice. Moreover, if $S M_{ξ}^{w} (X)$ contains an increasing sequence of length ω then it contains an increasing sequence of length ω₁. Finally, if $S M_{ξ}^{w} (X)$ is uncountable, then it contains an antichain...

Universal embeddings of $l^{1} (α)$ into the space of continuous functions on a product space

N. Kalamidas, Th. Zachariades (1989)

Colloquium Mathematicae

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Some types of points in $N^{*}$

Gryzlov, A.

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Internally club and approachable for larger structures

John Krueger (2008)

Fundamenta Mathematicae

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We generalize the notion of a fat subset of a regular cardinal κ to a fat subset of $P_{κ} (X)$ , where κ ⊆ X. Suppose μ < κ, $μ^{< μ} = μ$ , and κ is supercompact. Then there is a generic extension in which κ = μ⁺⁺, and for all regular λ ≥ μ⁺⁺, there are stationarily many N in ${[H (λ)]}^{μ ⁺}$ which are internally club but not internally approachable.

Logarithmically improved blow-up criterion for smooth solutions to the Leray- $α$ -magnetohydrodynamic equations

Ines Ben Omrane, Sadek Gala, Jae-Myoung Kim, Maria Alessandra Ragusa (2019)

Archivum Mathematicum

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In this paper, the Cauchy problem for the $3 D$ Leray- $α$ -MHD model is investigated. We obtain the logarithmically improved blow-up criterion of smooth solutions for the Leray- $α$ -MHD model in terms of the magnetic field $B$ only in the framework of homogeneous Besov space with negative index.

Generic extensions of models of ZFC

Lev Bukovský (2017)

Commentationes Mathematicae Universitatis Carolinae

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The paper contains a self-contained alternative proof of my Theorem in Characterization of generic extensions of models of set theory, Fund. Math. 83 (1973), 35–46, saying that for models $M \subseteq N$ of ZFC with same ordinals, the condition $A p r_{M, N} (κ)$ implies that $N$ is a $κ$ -C.C. generic extension of $M$ .

Artinian automorphisms of infinite groups

Antonella Leone (2006)

Bollettino dell'Unione Matematica Italiana

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An automorphism a of a group G is called an artinian automorphism if for every strictly descending chain $H_{1}>H_{2}>\cdots>H_{n}>\cdots$ of subgroups of G there exists a positive integer $m$ such that $(H_{n})^{a}=H_{n}$ for every $n\geq m$ . In this paper we show that in many cases the group of all artinian automorphisms of $G$ coincides with the group of all power automorphisms of $G$ .

Displaying similar documents to “P-NDOP and P-decompositions of ℵ ϵ -saturated models of superstable theories”

Displaying similar documents to “P-NDOP and P-decompositions of $ℵ_{ϵ}$ -saturated models of superstable theories”