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Displaying 581 – 600 of 729

On the Leibniz congruences

Josep Font (1993)

Banach Center Publications

The aim of this paper is to discuss the motivation for a new general algebraic semantics for deductive systems, to introduce it, and to present an outline of its main features. Some tools from the theory of abstract logics are also introduced, and two classifications of deductive systems are analysed: one is based on the behaviour of the Leibniz congruence (the maximum congruence of a logical matrix) and the other on the behaviour of the Frege operator (which associates to every theory the interderivability...

On the Leibniz-Mycielski axiom in set theory

Ali Enayat (2004)

Fundamenta Mathematicae

Motivated by Leibniz’s thesis on the identity of indiscernibles, Mycielski introduced a set-theoretic axiom, here dubbed the Leibniz-Mycielski axiom LM, which asserts that for each pair of distinct sets x and y there exists an ordinal α exceeding the ranks of x and y, and a formula φ(v), such that $(V_{α}, \in)$ satisfies φ(x) ∧¬ φ(y). We examine the relationship between LM and some other axioms of set theory. Our principal results are as follows: 1. In the presence of ZF, the following are equivalent: (a) LM. (b)...

On the lengths of bad sequences of monomial ideals over polynomial rings

Florian Pelupessy, Andreas Weiermann (2012)

Fundamenta Mathematicae

We give bad (with respect to the reverse inclusion ordering) sequences of monomial ideals in two variables with Ackermannian lengths and extend this to multiple recursive lengths for more variables.

On The Limits Of The Families Of Lindenbaum Algebras

Slobodan T. Vujošević (1979)

Publications de l'Institut Mathématique

On the Maćkowiak-Tymchatyn theorem

Klaas Pieter Hart, B. J. van der Steeg (2002)

Acta Universitatis Carolinae. Mathematica et Physica

On the metamathematics of impredicative set theory [Book]

W. Marek (1973)

On the metric reflection of a pseudometric space in ZF

Horst Herrlich, Kyriakos Keremedis (2015)

Commentationes Mathematicae Universitatis Carolinae

We show: (i) The countable axiom of choice $𝐂𝐀𝐂$ is equivalent to each one of the statements: (a) a pseudometric space is sequentially compact iff its metric reflection is sequentially compact, (b) a pseudometric space is complete iff its metric reflection is complete. (ii) The countable multiple choice axiom $𝐂𝐌𝐂$ is equivalent to the statement: (a) a pseudometric space is Weierstrass-compact iff its metric reflection is Weierstrass-compact. (iii) The axiom of choice $𝐀𝐂$ is equivalent to each one of the...

On the model companion for e-fold p-adically valued fields.

Ido Efrat (1991)

Manuscripta mathematica

On the multiple Birkhoff recurrence theorem in dynamics

Bohuslav Balcar, Pavel Kalášek, Scott W. Williams (1987)

Commentationes Mathematicae Universitatis Carolinae

On the non-existence of certain group topologies

Christian Rosendal (2005)

Fundamenta Mathematicae

Minimal Hausdorff (Baire) group topologies of certain groups of transformations naturally occurring in analysis are studied. The results obtained are subsequently applied to show that, e.g., the homeomorphism groups of the rational and of the irrational numbers carry no Polish group topology. In answer to a question of A. S. Kechris it is shown that the group of Borel automorphisms of ℝ cannot be a Polish group either.

On the non-extendibility of strongness and supercompactness through strong compactness

Arthur W. Apter (2002)

Fundamenta Mathematicae

If κ is either supercompact or strong and δ < κ is α strong or α supercompact for every α < κ, then it is known δ must be (fully) strong or supercompact. We show this is not necessarily the case if κ is strongly compact.

On the nontrivial solvability of systems of homogeneous linear equations over $ℤ$ in ZFC

Jan Šaroch (2020)

Commentationes Mathematicae Universitatis Carolinae

Motivated by the paper by H. Herrlich, E. Tachtsis (2017) we investigate in ZFC the following compactness question: for which uncountable cardinals $κ$ , an arbitrary nonempty system $S$ of homogeneous $ℤ$ -linear equations is nontrivially solvable in $ℤ$ provided that each of its subsystems of cardinality less than $κ$ is nontrivially solvable in $ℤ$ ?

On the notion of Fuzzy Set.

Nando Prati (1992)

Stochastica

Many discussions have been made on the problem of(i) What are Fuzzy Sets?since the origin of the theory. Due to the structure of Fuzzy Sets the first impression that many people have is that Fuzzy Sets are the distribution of a probability. Recent developments of many theories of uncertainty measures (belief functions, possibility and fuzzy measures, capacities) can make also think that a Fuzzy Set is the distribution of an uncertainty measure. Other problems arising inside the theory of Fuzzy Sets...

On the number of closed subsets of linear functions in the 6-valued logic

D. Lau, B. Schröder (1991)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

On the number of countable models of complete theories with finite Rudin-Keisler preorders.

Sudoplatov, S.V. (2007)

Sibirskij Matematicheskij Zhurnal

On the number of countable models of stable theories

Predrag Tanović (2001)

Fundamenta Mathematicae

We prove: Theorem. If T is a countable, complete, stable, first-order theory having an infinite set of constants with different interpretations, then I(T,ℵ₀) ≥ ℵ₀.

On the number of generic models

Vincent Lee, Mark Nadel (1975)

Fundamenta Mathematicae

On the number of models of the Kelley-Morse theory of classes

W. Marek, Paweł Zbierski (1980)

Fundamenta Mathematicae

On the number of monotonic functions from two-valued logic to $k$ -valued logic

Juraj Hromkovič (1985)

Kybernetika

On the number of non-isomorphic subspaces of a Banach space

Valentin Ferenczi, Christian Rosendal (2005)

Studia Mathematica

We study the number of non-isomorphic subspaces of a given Banach space. Our main result is the following. Let be a Banach space with an unconditional basis ${(e_{i})}_{i \in ℕ}$ ; then either there exists a perfect set P of infinite subsets of ℕ such that for any two distinct A,B ∈ P, ${[e_{i}]}_{i \in A} ≇ {[e_{i}]}_{i \in B}$ , or for a residual set of infinite subsets A of ℕ, ${[e_{i}]}_{i \in A}$ is isomorphic to , and in that case, is isomorphic to its square, to its hyperplanes, uniformly isomorphic to $\oplus {[e_{i}]}_{i \in D}$ for any D ⊂ ℕ, and isomorphic to a denumerable Schauder decomposition...

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