Editing Model Theory (section)

== <span style="color: #FFFFFF;">Applying</span> ==
'''Modeling 'Satisfiability' (The Truth Checker):'''
<syntaxhighlight lang="python">
def is_model_valid(domain, relation_func, statement):
    """
    Checks if a 'World' satisfies a 'Sentence'.
    Sentence: 'For all x, x is even'
    """
    for x in domain:
        if not relation_func(x):
            print(f"Counter-example found: {x}")
            return False
    return True

# World: The set {2, 4, 6}
# Relation: Is even?
print(f"Does the world satisfy 'All Even'? {is_model_valid([2,4,6], lambda x: x%2==0, 'All Even')}")
# Model theory is the basis for 'Formal Verification' 
# in chip design and software.
</syntaxhighlight>

; Model Theory Milestones
: '''The Compactness Theorem''' → If every finite subset of a theory has a model, then the whole theory has a model. (The "Bridge" to infinity).
: '''Robinson's Non-Standard Analysis''' → Using model theory to bring back "Infinitesimals" and prove they are logically sound.
: '''Ax-Kochen Theorem''' → A famous proof in algebra that was solved using model theory, showing that logic can solve "Pure" math problems.
: '''O-Minimality''' → A modern branch of model theory used to study geometry and tame "chaotic" functions.
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