Scheme representation for first-order logic

4 pages•Published: July 28, 2014

Abstract

My research concerns a construction of "logical schemes," geometric entities
which represent logical theories in much the same way that algebraic schemes
represent rings. These involve two components: a semantic spectral space
and a syntactic structure sheaf. As in the algebraic case, we can recover a
theory from its scheme representation (up to a conservative completion) and
the structure sheaf is local in a certain logical sense. From these ane pieces
we can build up a 2-category of logical schemes which share some of the nice
properties of algebraic schemes.

Keyphrases: category theory, first order logic, stone type dualities

In: Nikolaos Galatos, Alexander Kurz and Constantine Tsinakis (editors). TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic, vol 25, pages 10-13.

Links:	https://easychair.org/publications/paper/dRJ
	https://doi.org/10.29007/8l5l

BibTeX entry

@inproceedings{TACL2013:Scheme_representation_first_order,
  author    = {Steve Awodey and Spencer Breiner},
  title     = {Scheme representation for first-order logic},
  booktitle = {TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic},
  editor    = {Nikolaos Galatos and Alexander Kurz and Constantine Tsinakis},
  series    = {EPiC Series in Computing},
  volume    = {25},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/dRJ},
  doi       = {10.29007/8l5l},
  pages     = {10-13},
  year      = {2014}}

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