We prove that, building upon the universal-existential orthogonality-based axiom system for metric planes presented in [28], one can provide universal-existential axiom systems – expressed solely in terms of the ternary predicate I, with I(abc) standing for ‘ab is congruent to ac’, which Pieri has introduced 100 years ago – for metric planes, for absolute geometry with the circle axiom, for Euc...

Tony Martin proved in [Mar98] that the Axiom of Determinacy AD implies the Axiom of Blackwell Determinacy Bl-AD, and conjectured that the converse holds as well: Conjecture 1 The Axiom of Blackwell Determinacy Bl-AD implies the Axiom of Determinacy AD. Although Martin, Neeman and Vervoort in their [MarNeeVer03] have made considerable progress on Martin’s Conjecture 1, the full conjecture remain...

Many consumers report that healthy eating is more expensive than unhealthy eating (the affordability axiom). We hypothesize that endorsement of this belief may be driven by the motivation to eat unhealthy foods. We tested this hypothesis in three studies. Study 1 revealed that the affordability axiom is associated with poorer eating habits and higher Body Mass Index (BMI). Study 2 found that th...

We propose that failures of the axiom of choice, that is, surjective functions admitting no sections, can be reasonably classified by means of invariants borrowed from algebraic topology. We show that cohomology, when defined so that its usual exactness properties hold even in the absence of the axiom of choice, is adequate for detecting failures of this axiom in the following sense. If a set X...

George Boolos has described an interpretation of a fragment of ZFC in a consistent second-order theory whose only axiom is a modification of Frege’s inconsistent Axiom V. We build on Boolos’s interpretation and study the models of a variety of such theories obtained by amending Axiom V in the spirit of the principle of limitation of size. After providing a complete structural description of all...

Zermelo in his remarkable 1930a offered his final axiomatization of set theory as well as a striking, synthetic view of a procession of natural models that would have a modern resonance. Appearing only six articles after Skolem 1930 in Fundamenta mathematicae, Zermelo’s article seemed strategically placed as a response, an aspect that we will discuss below, but its dramatically new picture of s...

The first part of the talk will highlight the way in which assumptions widespread in the literature on reasoning about knowledge generate the traditional philosophical problem of scepticism. The problematic assumptions to be discussed here do not include logical omniscience, but are equally serious. My particular concern will be with the so-called Brouwerian axiom: p $ K~Kp (if p is false, an a...

A logical physical ontology is code theory, wherein reality is neither deterministic nor random. In light of Conway and Kochen’s free will theorem [1] and strong free will theorem [2], we discuss the plausibility of a third axiomatic option geometric language; the code theoretic axiom. We suggest freewill choices at the syntactically free steps of a geometric language of spacetime form the code...

This paper investigates the univalence axiom in intensional Martin-Löf type theory. In particular, it looks at how univalence can be derived from simpler axioms. We first present some existing work, collected together from various published and unpublished sources; we then we present a new decomposition of the univalence axiom into simpler axioms. We argue that these axioms are easier to verify...