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Countable Models
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Concept
Löwenheim-Skolem Theorem
The
Löwenheim-Skolem Theorem
asserts that if a
first-order theory
has an
infinite model
, then it has
models of every infinite cardinality
. This theorem highlights the
limitations of first-order logic
in characterizing the
size of infinite structures
, leading to the
Skolem paradox
where
countable models
can exist for
uncountable theories
.
3