5 citations · 11 across the 9 of their papers we have counts for
9 papers
The magmatic universe revisited: we define ordered pairs, relations, numbers and a special form of Separation
Athanassios Tzouvaras
This is a companion article to \cite{Tz24}. We address the following two questions: 1) Can we define in the magmatic universe of \cite{Tz24} counterparts, or just analogues, of…
An observer-based approach to the sorites paradox and the logic derived from that
Athanassios Tzouvaras
We approach the sorites paradox (SP) through an observer-based and time-dependent approach to truth of vague assertions. Formally the approach gives rise to a semantics, called flu…
Asymptotic typicality degrees of properties over finite structures
Athanassios Tzouvaras
In previous work we defined and studied a notion of typicality, originated with B. Russell, for properties and objects in the context of general infinite first-order structures. In…
Large transitive models in local {\rm ZFC}
Athanassios Tzouvaras
This paper is a sequel to \cite{Tz10}, where a local version of ZFC, LZFC, was introduced and examined and transitive models of ZFC with properties that resemble large cardinal pro…
Localizing the axioms
Athanassios Tzouvaras
We examine what happens if we replace ZFC with a localistic/relativistic system, LZFC, whose central new axiom, denoted by , says that every set belongs to a transi…
Consequences of Vopěnka's Principle over weak set theories
Athanassios Tzouvaras
It is shown that Vopěnka's Principle (VP) can restore almost the entire ZF over a weak fragment of it. Namely, if EST is the theory consisting of the axioms of Extensionality, Empt…