A recursion-theoretic characterization of instances of $ΒΣ_n$ provable in $П_{n+1}(N)$

Zofia Adamowicz

Displaying similar documents to “A recursion-theoretic characterization of instances of $Β Σ_{n}$ provable in $П_{n + 1} (N)$ ”

A Hanf number for saturation and omission

John T. Baldwin, Saharon Shelah (2011)

Fundamenta Mathematicae

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Suppose t = (T,T₁,p) is a triple of two countable theories T ⊆ T₁ in vocabularies τ ⊂ τ₁ and a τ₁-type p over the empty set. We show that the Hanf number for the property ’there is a model M₁ of T₁ which omits p, but M₁ ↾ τ is saturated’ is essentially equal to the Löwenheim number of second order logic. In Section 4 we make exact computations of these Hanf numbers and note some distinctions between ’first order’ and ’second order quantification’. In particular, we show that if κ is...

On normalization of proofs in set theory

Lars Hallnäs

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CONTENTSIntroduction..............................................................................................................................................5I. Naive set theory.....................................................................................................................................61. The formal system................................................................................................................................62. Inversion and reduction...

Provident sets and rudimentary set forcing

A. R. D. Mathias (2015)

Fundamenta Mathematicae

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Using the theory of rudimentary recursion and provident sets expounded in [MB], we give a treatment of set forcing appropriate for working over models of a theory PROVI which may plausibly claim to be the weakest set theory supporting a smooth theory of set forcing, and of which the minimal model is Jensen’s $J_{ω}$ . Much of the development is rudimentary or at worst given by rudimentary recursions with parameter the notion of forcing under consideration. Our development eschews the power...

A characterization of almost continuity and weak continuity

Chrisostomos Petalas, Theodoros Vidalis (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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It is well known that a function $f$ from a space $X$ into a space $Y$ is continuous if and only if, for every set $K$ in $X$ the image of the closure of $K$ under $f$ is a subset of the closure of the image of it. In this paper we characterize almost continuity and weak continuity by proving similar relations for the subsets $K$ of $X$ .

The gap between I₃ and the wholeness axiom

Paul Corazza (2003)

Fundamenta Mathematicae

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∃κI₃(κ) is the assertion that there is an elementary embedding $i : V_{λ} \to V_{λ}$ with critical point below λ, and with λ a limit. The Wholeness Axiom, or WA, asserts that there is a nontrivial elementary embedding j: V → V; WA is formulated in the language ∈,j and has as axioms an Elementarity schema, which asserts that j is elementary; a Critical Point axiom, which asserts that there is a least ordinal moved by j; and includes every instance of the Separation schema for j-formulas. Because no instance...

On $ω^{2}$ -saturated families

Lajos Soukup (1991)

Commentationes Mathematicae Universitatis Carolinae

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If there is no inner model with measurable cardinals, then for each cardinal $λ$ there is an almost disjoint family $𝒜_{λ}$ of countable subsets of $λ$ such that every subset of $λ$ with order type $\geq ω^{2}$ contains an element of $𝒜_{λ}$ .

The almost Daugavet property and translation-invariant subspaces

Simon Lücking (2014)

Colloquium Mathematicae

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Let G be a metrizable, compact abelian group and let Λ be a subset of its dual group Ĝ. We show that $C_{Λ} (G)$ has the almost Daugavet property if and only if Λ is an infinite set, and that $L ¹_{Λ} (G)$ has the almost Daugavet property if and only if Λ is not a Λ(1) set.

Set theories incorporating Hilbert's ε-symbol

T. B. Flannagan

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CONTENTS§ 1. Introduction ............................................................................................................ 5§ 2. The ε-calculus for є............................................................................................ 6§ 3. Reflection principles in e-set theories.............................................................. 6§ 4. [E]-elementary chains.......................................................................................... 11§ 5. Forcing...

Comparing the closed almost disjointness and dominating numbers

Dilip Raghavan, Saharon Shelah (2012)

Fundamenta Mathematicae

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We prove that if there is a dominating family of size ℵ₁, then there are ℵ₁ many compact subsets of $ω^{ω}$ whose union is a maximal almost disjoint family of functions that is also maximal with respect to infinite partial functions.

A note on an approximative scheme of finding almost homoclinic solutions for Newtonian systems

Robert Krawczyk (2014)

Banach Center Publications

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In this work we will be concerned with the existence of almost homoclinic solutions for a Newtonian system $q ̈ + \nabla_{q} V (t, q) = f (t)$ , where t ∈ ℝ, q ∈ ℝⁿ. It is assumed that a potential V: ℝ × ℝⁿ → ℝ is C¹-smooth and its gradient map $\nabla_{q} V : ℝ \times ℝ ⁿ \to ℝ ⁿ$ is bounded with respect to t. Moreover, a forcing term f: ℝ → ℝⁿ is continuous, bounded and square integrable. We will show that the approximative scheme due to J. Janczewska (see [J2]) for a time periodic potential extends to our case.

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...

Axioms weaker then $R_{0}$

J. Guia (1984)

Matematički Vesnik

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Induced almost continuous functions on hyperspaces

Alejandro Illanes (2006)

Colloquium Mathematicae

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For a metric continuum X, let C(X) (resp., $2^{X}$ ) be the hyperspace of subcontinua (resp., nonempty closed subsets) of X. Let f: X → Y be an almost continuous function. Let C(f): C(X) → C(Y) and $2^{f} : 2^{X} \to 2^{Y}$ be the induced functions given by $C (f) (A) = c l_{Y} (f (A))$ and $2^{f} (A) = c l_{Y} (f (A))$ . In this paper, we prove that: • If $2^{f}$ is almost continuous, then f is continuous. • If C(f) is almost continuous and X is locally connected, then f is continuous. • If X is not locally connected, then there exists an almost continuous function f: X → [0,1]...

Asymmetric tie-points and almost clopen subsets of $ℕ^{*}$

Alan S. Dow, Saharon Shelah (2018)

Commentationes Mathematicae Universitatis Carolinae

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A tie-point of compact space is analogous to a cut-point: the complement of the point falls apart into two relatively clopen non-compact subsets. We review some of the many consistency results that have depended on the construction of tie-points of $ℕ^{*}$ . One especially important application, due to Veličković, was to the existence of nontrivial involutions on $ℕ^{*}$ . A tie-point of $ℕ^{*}$ has been called symmetric if it is the unique fixed point of an involution. We define the notion of an almost...

Uncountable cardinals have the same monadic ∀₁¹ positive theory over large sets

Athanassios Tzouvaras (2004)

Fundamenta Mathematicae

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We show that uncountable cardinals are indistinguishable by sentences of the monadic second-order language of order of the form (∀X)ϕ(X) and (∃X)ϕ(X), for ϕ positive in X and containing no set-quantifiers, when the set variables range over large (= cofinal) subsets of the cardinals. This strengthens the result of Doner-Mostowski-Tarski [3] that (κ,∈), (λ,∈) are elementarily equivalent when κ, λ are uncountable. It follows that we can consistently postulate that the structures $(2^{κ}, {[2^{κ}]}^{> κ}, <)$ , $(2^{λ}, {[2^{λ}]}^{> λ}, <)$ are...

Almost continuous functions on $I^{n}$

Kenneth Kellum (1973)

Fundamenta Mathematicae

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Maximal almost disjoint families of functions

Dilip Raghavan (2009)

Fundamenta Mathematicae

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We study maximal almost disjoint (MAD) families of functions in $ω^{ω}$ that satisfy certain strong combinatorial properties. In particular, we study the notions of strongly and very MAD families of functions. We introduce and study a hierarchy of combinatorial properties lying between strong MADness and very MADness. Proving a conjecture of Brendle, we show that if $c o v (ℳ) <_{}$ , then there no very MAD families. We answer a question of Kastermans by constructing a strongly MAD family from = . Next, we...

Displaying similar documents to “A recursion-theoretic characterization of instances of Β Σ n provable in П n + 1 ( N ) ”

Displaying similar documents to “A recursion-theoretic characterization of instances of $Β Σ_{n}$ provable in $П_{n + 1} (N)$ ”