## 119 Citations

Unconscious Foundations of Mathematics

- Philosophy
- 2021

Mathematics accompanies throughout history the development of critical thinking, of philosophy, of physics and of the wide majority of modern research and technologies: in short, mathematics…

The Theory of Finitely Supported Structures and Choice Forms

- Computer Science, MathematicsSci. Ann. Comput. Sci.
- 2018

The results presented in this paper include the meta-theoretical presentation of finitely supported structures, the study of the consistency of choice principles (and of results requiring choice principles) within this framework, and the presentation of several connections with other topics.

Dening Finitely Supported Mathematics over Sets with Atoms

- MathematicsICTERI
- 2015

This paper presents some steps of defining a finitely supported mathematics by using sets with atoms. Such a mathematics generalizes the classical Zermelo-Fraenkel mathematics, and represents an…

Fraenkel's Axiom of Restriction: axiom choice, intended models, and categoricity

- Economics
- 2010

A recent debate has focused on different methodological principles underlying the practice of axiom choice in mathematics (cf. Feferman et al., 2000; Maddy, 1997; Easwaran, 2008). The general aim of…

Ontology and the foundations of mathematics

- Philosophy
- 1999

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 1999.

How critical is “critical thinking”?

- Philosophy
- 2016

Before criticism is justified, an account of the applicable criteria should be given. This task concerns first of all the well-known logical principles of identity, contradiction and the excluded…

Static Analysis in Finitely Supported Mathematics

- Mathematics2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)
- 2015

A theory of abstract interpretations which is consistent to the principles of constructing the Finitely Supported Mathematics is developed, and some widening and narrowing techniques are provided in order to approximate the least fixedpoints of finitely supported transition functions.

On the Axiom of Canonicity

- PhilosophyLogic and Logical Philosophy
- 2022

The axiom of canonicity was introduced by the famous Polish logician Roman Suszko in 1951 as an explication of Skolem's Paradox (without reference to the L\"{o}wenheim-Skolem theorem) and a precise…

Game semantics of universes

- Computer ScienceArXiv
- 2022

This extension completes game semantics of all standard types of Martin-L¨of type theory for the first time in the 30 years history of modern game semantics and makes the powerful combinatorial reasoning of game semantics available for the study of universes and types generated by them.

## References

Untersuchungen über die Grundlagen der Mengenlehre. I

- Mathematics
- 1908

----------------------------------------------------Nutzungsbedingungen DigiZeitschriften e.V. gewährt ein nicht exklusives, nicht übertragbares, persönliches und beschränktes Recht auf Nutzung…