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An investigation into the non-constructive parts of proving completeness for first-order logic

Carlsson, Hugo Carl Samuel LU (2024) In Bachelor's Theses in Mathematical Sciences MATK11 20241
Mathematics (Faculty of Engineering)
Mathematics (Faculty of Sciences)
Centre for Mathematical Sciences
Abstract
This thesis will be an investigation into different proofs of Completeness in first-order logic. Particular attention will be put on analyzing the role of the Ultrafilter Lemma and its necessity in proving
the Completeness Theorem. An attempt will be made to develop a
proof that separates out this non-constructive aspect, but still uses
the law of excluded middle. The overall aim is to understand why and
when non-constructive arguments are needed. Different proofs of the
theorem will then be showcased and compared, and equivalents of the
Completeness Theorem will be discussed.
Please use this url to cite or link to this publication:
author
Carlsson, Hugo Carl Samuel LU
supervisor
organization
course
MATK11 20241
year
type
M2 - Bachelor Degree
subject
keywords
Mathematics, Logic, Mathematical logic, First-order logic, Completeness, Gödel, non-constructive, proof, Ultrafilter lemma
publication/series
Bachelor's Theses in Mathematical Sciences
report number
LUNFMA-4164-2024
ISSN
1654-6229
other publication id
2024:K6
language
English
id
9151713
date added to LUP
2024-12-05 16:05:19
date last changed
2024-12-05 16:05:19
@misc{9151713,
  abstract     = {{This thesis will be an investigation into different proofs of Completeness in first-order logic. Particular attention will be put on analyzing the role of the Ultrafilter Lemma and its necessity in proving
the Completeness Theorem. An attempt will be made to develop a
proof that separates out this non-constructive aspect, but still uses
the law of excluded middle. The overall aim is to understand why and
when non-constructive arguments are needed. Different proofs of the
theorem will then be showcased and compared, and equivalents of the
Completeness Theorem will be discussed.}},
  author       = {{Carlsson, Hugo Carl Samuel}},
  issn         = {{1654-6229}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Bachelor's Theses in Mathematical Sciences}},
  title        = {{An investigation into the non-constructive parts of proving completeness for first-order logic}},
  year         = {{2024}},
}