The Axiom of Choice in Quine's New Foundations for Mathematical Logic

The Axiom of Choice in Quine's New Foundations for Mathematical Logic.

The Axiom of Choice in the Foundations of Mathematics

The principle of set theory known as the Axiom of Choice (AC) has been hailed as “probably the most interesting and, in spite of its late appearance, the most discussed axiom of mathematics, second only to Euclid’s axiom of parallels which was introduced more than two thousand years ago”1 It has been employed in countless mathematical papers, a number of monographs have been exclusively devoted...

study of cohesive devices in the textbook of english for the students of apsychology by rastegarpour

this study investigates the cohesive devices used in the textbook of english for the students of psychology. the research questions and hypotheses in the present study are based on what frequency and distribution of grammatical and lexical cohesive devices are. then, to answer the questions all grammatical and lexical cohesive devices in reading comprehension passages from 6 units of 21units th...

The Significance of Aristotle's Particularisation in the Foundations of Mathematics, Logic and Computability: Cohen and the Axiom of Choice

The logic underlying our current interpretations of all first-order formal languages—which provide the formal foundations for all computing languages—is Aristotle’s logic of predicates. I show, first, that a fundamental tenet of this logic, namely Aristotlean particularisation, is a subjective, and objectively unverifiable, postulation that is ‘stronger’ than the Axiom of Choice; and that, seco...

The Axiom of Choice and Combinatory Logic (preliminary Draft)

We combine a variety of constructive methods (including forcing, realizability, asymmetric interpretation), to obtain consistency results concerning combinatory logic with extensionality and (forms of) the axiom of choice. §1. The problem. It is well-known that combinatory logic is inconsistent with the choice schema ACV for operations: (∀x)(∃y)A(x, y)→ (∃f)(∀x)A(x, fx) (1) where A is an arbitr...