AbstractWe develop an axiomatic set theory — the Theory of Hyperfinite Sets THS— which is based on the idea of the existence of proper subclasses of large finite sets. We demonstrate how theorems of classical continuous mathematics can be transfered to THS, prove consistency of THS, and present some applications
The theory presented here stemmed from years of teaching analysis at pre-university level first usin...
Wilhelm Ackermann has proved that Zermelo-Fraenkel set theory in which the axiom of infinity is repl...
In set theory [1], two sets are considered to have the same cardinality, if a one-to-one corresponde...
AbstractWe develop an axiomatic set theory — the Theory of Hyperfinite Sets THS— which is based on t...
In this paper intuitionistic set theory INC# in infinitary set theoretical language is considered. ...
Main results are: (i) number e^{e} is transcendental; (ii) the both numbers e+π and e-π are irratio...
In this paper we propose a reflection on the use of axiomatic set theory as a fundamental tool to ad...
Often, people who study mathematics learn theorems to prove results in and about the vast array of b...
It is known that the Infinity Axiom can be expressed, even if the Axiom of Foundation is not assumed...
The standard elementary number theory is not a finite axiomatic system due to the presence of the in...
This dissertation is a conceptual history of transfinite set theory from the earliest results until ...
Set theory deals with the most fundamental existence questions in mathematics– questions which affect...
The foundation of analysis does not require the full generality of set theory but can be accomplishe...
We give a new set theoretic system of axioms motivated by a topological intuition: The set of subset...
The infinite in mathematics has two manifestations. Its occurrence in analysis has been satisfactori...
The theory presented here stemmed from years of teaching analysis at pre-university level first usin...
Wilhelm Ackermann has proved that Zermelo-Fraenkel set theory in which the axiom of infinity is repl...
In set theory [1], two sets are considered to have the same cardinality, if a one-to-one corresponde...
AbstractWe develop an axiomatic set theory — the Theory of Hyperfinite Sets THS— which is based on t...
In this paper intuitionistic set theory INC# in infinitary set theoretical language is considered. ...
Main results are: (i) number e^{e} is transcendental; (ii) the both numbers e+π and e-π are irratio...
In this paper we propose a reflection on the use of axiomatic set theory as a fundamental tool to ad...
Often, people who study mathematics learn theorems to prove results in and about the vast array of b...
It is known that the Infinity Axiom can be expressed, even if the Axiom of Foundation is not assumed...
The standard elementary number theory is not a finite axiomatic system due to the presence of the in...
This dissertation is a conceptual history of transfinite set theory from the earliest results until ...
Set theory deals with the most fundamental existence questions in mathematics– questions which affect...
The foundation of analysis does not require the full generality of set theory but can be accomplishe...
We give a new set theoretic system of axioms motivated by a topological intuition: The set of subset...
The infinite in mathematics has two manifestations. Its occurrence in analysis has been satisfactori...
The theory presented here stemmed from years of teaching analysis at pre-university level first usin...
Wilhelm Ackermann has proved that Zermelo-Fraenkel set theory in which the axiom of infinity is repl...
In set theory [1], two sets are considered to have the same cardinality, if a one-to-one corresponde...
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