Register to reply

Compactness theorem proof

by rainwyz0706
Tags: compactness, proof, theorem
Share this thread:
rainwyz0706
#1
Jun6-10, 04:28 PM
P: 36
An expression of the compactness theorem for sets of sentences is that: let T be a set of sentences in L. Then T has a model iff every finite subset of T has a model.
Could anyone give me some hints how to prove this?
The first direction is straightforward: every model of T is a model of every subset of T. But what about the opposite direction? Any help is appreciated!
Phys.Org News Partner Science news on Phys.org
Scientists discover RNA modifications in some unexpected places
Scientists discover tropical tree microbiome in Panama
'Squid skin' metamaterials project yields vivid color display
JSuarez
#2
Jun6-10, 06:26 PM
P: 402
My advice would be to not try to reinvent the wheel, and study the proofs given in any logic textbook.


Register to reply

Related Discussions
Compactness Proof w/o Heine-Borel Calculus & Beyond Homework 7
Proof using mean-value theorem Calculus & Beyond Homework 1
Analysis - compactness and sequentially compactness Calculus & Beyond Homework 1
Proof of the mean value theorem Calculus & Beyond Homework 9
Analysis / compactness proof check Calculus 6