homework01 - A B C then A C . 3. Show that if A B C then A...

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Math 5020 Homework 1 due Friday, February 11 Throughout the homework assignment, unless otherwise specified, we fix a first-order language L and assume all structures are L -structures. 1. Show that A B iff for any quantifier-free L -formula φ ( x 1 , . . . , x n ) and a 1 , . . . , a n ∈ | A | , A | = φ [ a 1 , . . . , a n ] ⇐⇒ B | = φ [ a 1 , . . . , a n ] . 2. Show that if
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Unformatted text preview: A B C then A C . 3. Show that if A B C then A C . 4. Finish the proof of the Upward LowenheimSkolem Theorem. That is, assuming A is an innite L-structure and an innite cardinality, nd an elementary extension of A of cardinality exactly ....
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This note was uploaded on 04/11/2011 for the course MATH 5020 taught by Professor Staff during the Spring '11 term at North Texas.

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