Axioms weaker then $R_{0}$

J. Guia

Displaying similar documents to “Axioms weaker then $R_{0}$ ”

Characterizations of some bitopological separation axioms in terms of $i j - θ$ - closure operator

S. K. Sen, J. N. Nandi, M. N. Mukherjee (1992)

Matematički Vesnik

Similarity:

$T_{i}$ - pairwise continuous functions and bitopological separation axioms

M. Jelić (1989)

Matematički Vesnik

Similarity:

The $S_{α}$ separation axioms

J. Guia (1986)

Matematički Vesnik

Similarity:

Axiom $T_{D}$ and the Simmons sublocale theorem

Jorge Picado, Aleš Pultr (2019)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

More precisely, we are analyzing some of H. Simmons, S. B. Niefield and K. I. Rosenthal results concerning sublocales induced by subspaces. H. Simmons was concerned with the question when the coframe of sublocales is Boolean; he recognized the role of the axiom $T_{D}$ for the relation of certain degrees of scatteredness but did not emphasize its role in the relation between sublocales and subspaces. S. B. Niefield and K. I. Rosenthal just mention this axiom in a remark about Simmons’ result....

Linear extenders and the Axiom of Choice

Marianne Morillon (2017)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

In set theory without the Axiom of Choice ZF, we prove that for every commutative field $𝕂$ , the following statement $𝐃_{𝕂}$ : “On every non null $𝕂$ -vector space, there exists a non null linear form” implies the existence of a “ $𝕂$ -linear extender” on every vector subspace of a $𝕂$ -vector space. This solves a question raised in Morillon M., Linear forms and axioms of choice, Comment. Math. Univ. Carolin. 50 (2009), no. 3, 421-431. In the second part of the paper, we generalize our results in the case...

A classification scheme for axioms weaker than $T_{0}$

G. Ervynck (1991)

Matematički Vesnik

Similarity:

The gap between I₃ and the wholeness axiom

Paul Corazza (2003)

Fundamenta Mathematicae

Similarity:

∃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...

Set theories incorporating Hilbert's ε-symbol

T. B. Flannagan

Similarity:

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...

On the Compactness and Countable Compactness of $2^{ℝ}$ in ZF

Kyriakos Keremedis, Evangelos Felouzis, Eleftherios Tachtsis (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

In the framework of ZF (Zermelo-Fraenkel set theory without the Axiom of Choice) we provide topological and Boolean-algebraic characterizations of the statements " $2^{ℝ}$ is countably compact" and " $2^{ℝ}$ is compact"

Essentially Incomparable Banach Spaces of Continuous Functions

Rogério Augusto dos Santos Fajardo (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

We construct, under Axiom ♢, a family ${(C (K_{ξ}))}_{ξ < 2^{(2^{ω})}}$ of indecomposable Banach spaces with few operators such that every operator from $C (K_{ξ})$ into $C (K_{η})$ is weakly compact, for all ξ ≠ η. In particular, these spaces are pairwise essentially incomparable. Assuming no additional set-theoretic axiom, we obtain this result with size $2^{ω}$ instead of $2^{(2^{ω})}$ .

On the Set-Theoretic Strength of Countable Compactness of the Tychonoff Product $2^{ℝ}$

Eleftherios Tachtsis (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

We work in ZF set theory (i.e., Zermelo-Fraenkel set theory minus the Axiom of Choice AC) and show the following: 1. The Axiom of Choice for well-ordered families of non-empty sets ( $A C^{W O}$ ) does not imply “the Tychonoff product $2^{ℝ}$ , where 2 is the discrete space 0,1, is countably compact” in ZF. This answers in the negative the following question from Keremedis, Felouzis, and Tachtsis [Bull. Polish Acad. Sci. Math. 55 (2007)]: Does the Countable Axiom of Choice for families of non-empty sets...

Propositional extensions of $L_{ω} 1_{ω}$

Richard Gostanian, Karel Hrbacek

Similarity:

CONTENTS0. Preliminaries....................................................................... 71. Adding propositional connectives to $L_{ω} 1_{ω}$ ............... 82. The propositional part of $L_{ω} 1_{ω}$ (S)............................. 103. The operation S and the Boolean algebra $B_{S}$ ............... 114. General model-theoretic properties of $L_{ω} 1_{ω}$ (S)...... 175. Hanf number computations...................................................... 226. Negative results for $L_{ω} 1_{ω}$ (S)...........................................

Covering Property Axiom $C P A_{c u b e}$ and its consequences

Krzysztof Ciesielski, Janusz Pawlikowski (2003)

Fundamenta Mathematicae

Similarity:

We formulate a Covering Property Axiom $C P A_{c u b e}$ , which holds in the iterated perfect set model, and show that it implies easily the following facts. (a) For every S ⊂ ℝ of cardinality continuum there exists a uniformly continuous function g: ℝ → ℝ with g[S] = [0,1]. (b) If S ⊂ ℝ is either perfectly meager or universally null then S has cardinality less than . (c) cof() = ω₁ < , i.e., the cofinality of the measure ideal is ω₁. (d) For every uniformly bounded sequence $⟨ f ₙ \in ℝ^{ℝ} ⟩_{n < ω}$ of Borel functions...

Possibly there is no uniformly completely Ramsey null set of size $2^{ω}$

Andrzej Nowik (2002)

Colloquium Mathematicae

Similarity:

We show that under the axiom $C P A_{c u b e}$ there is no uniformly completely Ramsey null set of size $2^{ω}$ . In particular, this holds in the iterated perfect set model. This answers a question of U. Darji.

An axiomatics of non-Desarguean geometry based on the half-plane as the primitive notion

A. Śniatycki

Similarity:

CONTENTSIntroduction................................................................................................................................................. 5PART I1. Axioms of Boolean algebra................................................................................................................. 62. Half-planes and their axioms.............................................................................................................. 73. The line.......................................................................................................................................................

On sentences provable in impredicative extensions of theories

Zygmunt Ratajczyk

Similarity:

CONTENTS0. Introduction.......................................................................... 51. Preliminaries............................................................................... 72. Basic facts to be used in the sequel....................................... 113. Predicates OD(.,.) and CL(.,.).................................................... 174. Predicate Sels............................................................................. 185. Strong $\sum_{n}^{1}$ -collection...........................................................

On certain non-constructive properties of infinite-dimensional vector spaces

Eleftherios Tachtsis (2018)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

In set theory without the axiom of choice ( $AC$ ), we study certain non-constructive properties of infinite-dimensional vector spaces. Among several results, we establish the following: (i) None of the principles AC $^{LO}$ (AC for linearly ordered families of nonempty sets)—and hence AC $^{WO}$ (AC for well-ordered families of nonempty sets)— $DC (< κ)$ (where $κ$ is an uncountable regular cardinal), and “for every infinite set $X$ , there is a bijection $f : X \to {0, 1} \times X$ ”, implies the statement “there exists a field $F$ such that...

Hyperplanes in matroids and the axiom of choice

Marianne Morillon (2022)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We show that in set theory without the axiom of choice ZF, the statement sH: “Every proper closed subset of a finitary matroid is the intersection of hyperplanes including it” implies AC $^{fin}$ , the axiom of choice for (nonempty) finite sets. We also provide an equivalent of the statement AC $^{fin}$ in terms of “graphic” matroids. Several open questions stay open in ZF, for example: does sH imply the axiom of choice?

On ultra-weak convergence in $L^{p}$

Donald E. Myers (1976)

Annales Polonici Mathematici

Similarity:

Lower and upper bounds for the provability of Herbrand consistency in weak arithmetics

Zofia Adamowicz, Konrad Zdanowski (2011)

Fundamenta Mathematicae

Similarity:

We prove that for i ≥ 1, the arithmetic $I Δ ₀ + Ω_{i}$ does not prove a variant of its own Herbrand consistency restricted to the terms of depth in $(1 + ε) l o g^{i + 2}$ , where ε is an arbitrarily small constant greater than zero. On the other hand, the provability holds for the set of terms of depths in $l o g^{i + 3}$ .

Displaying similar documents to “Axioms weaker then R 0 ”

Displaying similar documents to “Axioms weaker then $R_{0}$ ”