5 citations · 17 across the 12 of their papers we have counts for
12 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…
Semantics for first-order superposition logic
Athanassios Tzouvaras
We investigate how the sentence choice semantics (SCS) for propositional superposition logic (PLS) developed in \cite{Tz17} could be extended so as to successfully apply to first-o…
Propositional superposition logic
Athanassios Tzouvaras
We extend classical Propositional Logic (PL) by adding a new primitive binary connective , intended to represent the "superposition" of sentences and , an operation mot…
Some structural similarities between uncountable sets, powersets and the universe
Athanassios Tzouvaras
We establish some similarities/analogies between uncountable cardinals or powersets and the class of all sets. They concern mainly the Boolean algebras , for a reg…
Russell's typicality as another randomness notion
Athanassios Tzouvaras
We reformulate slightly Russell's notion of typicality, so as to eliminate its circularity and make it applicable to elements of any first-order structure. We argue that the notion…
Typicality à la Russell in set theory
Athanassios Tzouvaras
We adjust the notion of typicality originated with Russell, which was introduced and studied in a previous paper for general first-order structures, to make it expressible in the l…
Sets with dependent elements: A formalization of Castoriadis' notion of magma
Athanassios Tzouvaras
We present a formalization of collections that Cornelius Castoriadis calls ``magmas'', especially the property which mainly characterizes them and distinguishes them from the usual…