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Axioms
Special Issues
Mathematical Logic and Applications
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Mathematical Logic and Applications

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Logic".

Deadline for manuscript submissions: closed (20 June 2023) | Viewed by 1652

Special Issue Editors

Dr. Andrei Alexandru

E-Mail Website
Guest Editor
Institute of Computer Science, Romanian Academy, 700505 Iaşi, Romania
Interests: mathematical logic; set theory; algebra
Special Issues, Collections and Topics in MDPI journals
Dr. Bogdan Aman

E-Mail Website
Guest Editor
Institute of Computer Science, Romanian Academy, 700505 Iaşi, Romania
Interests: process algebra; type systems; membrane computing; reversible computing
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Gabriel Ciobanu

E-Mail Website
Guest Editor
Member of Academia Europaea, and Romanian Academy Iasi Branch, 700505 Iasi, Romania
Interests: computer science; logic; algebra
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

It is our pleasure to announce the launch of our Special Issue,  “Mathematical Logic and Applications”. With this Special Issue, our goal is to offer contributing authors the opportunity to publish their recent results ​on mathematical logic and the foundations of mathematics. ​Particularly, we are interested in papers covering the following topics: set theory, model theory, proof theory, recursion theory, or algebraic logic. Contributions from related areas, such as philosophy or theoretical computer science (including but not limited to rewriting systems, reversibility, programming language semantics, fuzzy logic, and modal logic or natural computing) are also welcome as long as mathematical logic methods are involved. Articles should be accessible to a large audience. 

If this initiative suits your interests, we encourage you to submit your current research to be included in this Special Issue.

Dr. Andrei Alexandru
Dr. Bogdan Aman
Prof. Dr. Gabriel Ciobanu
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • general logic
  • set theory
  • axiomatic systems
  • model theory
  • proof theory
  • algebraic logic
  • recursion
  • theoretical computer science

Published Papers (1 paper)

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Research

12 pages, 454 KiB  
Article
A Model in Which Well-Orderings of the Reals Appear at a Given Projective Level
by Vladimir Kanovei and Vassily Lyubetsky
Axioms 2022, 11(8), 354; https://doi.org/10.3390/axioms11080354 - 22 Jul 2022
Cited by 3 | Viewed by 1137
Abstract
The problem of the existence of analytically definable well-orderings at a given level of the projective hierarchy is considered. This problem is important as a part of the general problem of the study of the projective hierarchy in the ongoing development of descriptive [...] Read more.
The problem of the existence of analytically definable well-orderings at a given level of the projective hierarchy is considered. This problem is important as a part of the general problem of the study of the projective hierarchy in the ongoing development of descriptive set theory. We make use of a finite support product of the Jensen-type forcing notions to define a model of set theory ZFC in which, for a given n>2, there exists a good Δn1 well-ordering of the reals but there are no such well-orderings in the class Δn−11. Therefore the existence of a well-ordering of the reals at a certain level n>2 of the projective hierarchy does not imply the existence of such a well-ordering at the previous level n−1. This is a new result in such a generality (with n>2 arbitrary), and it may lead to further progress in studies of the projective hierarchy. Full article
(This article belongs to the Special Issue Mathematical Logic and Applications)
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