Displaying similar documents to “Definitions of finiteness based on order properties”

On a Certain Notion of Finite and a Finiteness Class in Set Theory without Choice

Horst Herrlich, Paul Howard, Eleftherios Tachtsis (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

We study the deductive strength of properties under basic set-theoretical operations of the subclass E-Fin of the Dedekind finite sets in set theory without the Axiom of Choice ( AC ), which consists of all E-finite sets, where a set X is called E-finite if for no proper subset Y of X is there a surjection f:Y → X.

Finiteness and choice

Omar De la Cruz (2002)

Fundamenta Mathematicae

Similarity:

We deal with weak choice principles of the form: Every "finite" family of non-empty sets has a choice function, where "finite" stands for one of several different definitions of finiteness that are not equivalent unless we assume the axiom of choice (AC). Several relations of implication and independence are established. In the process, we answer a few open questions about the relations between different definitions of finiteness.

Internal and forcing models for the impredicative theory of classes

Rolando Chuaqui

Similarity:

CONTENTSIntroduction............................................................................................................ 5I. Axiom system and elementary consequences........................................... 61. Axioms........................................................................................................................ 62. Definitions and elementary consequences........................................................ 9II. Principles of definitions by recursion..............................................................

There is no complete axiom system for shuffle expressions

A. Szepietowski (2010)

RAIRO - Theoretical Informatics and Applications

Similarity:

In this paper we show that neither the set of all valid equations between shuffle expressions nor the set of schemas of valid equations is recursively enumerable. Thus, neither of the sets can be recursively generated by any axiom system.

On partial orderings having precalibre-ℵ₁ and fragments of Martin's axiom

Joan Bagaria, Saharon Shelah (2016)

Fundamenta Mathematicae

Similarity:

We define a countable antichain condition (ccc) property for partial orderings, weaker than precalibre-ℵ₁, and show that Martin's axiom restricted to the class of partial orderings that have the property does not imply Martin's axiom for σ-linked partial orderings. This yields a new solution to an old question of the first author about the relative strength of Martin's axiom for σ-centered partial orderings together with the assertion that every Aronszajn tree is special. We also answer...