Construct Theories for Which the Following Interpretation Is a Model

question 140

Essay

construct theories for which the following interpretation is a model (i.e. construct at least two sentences which are true under the given interpretation).
Domain = {1, 2, 3, ..., 28, 29, 30}
a = 1 e = 21
b = 2 f = 23
c = 4 g = 27
d = 19 h = 29
Ex = {2, 4, 6, ..., 28, 30}
Ox = {1, 3, 5, ..., 27, 29}
Px = (2, 3, 5, 7, 11, 13, 17, 19, 23, 29}
Sxyz = The set of all triples such that the first is the sum of the second and third
{<2, 1, 1>, <3, 1, 2>, <3, 2, 1>, <4, 1, 3>, <4, 2, 2>, <4, 3, 1>, <5, 1, 4>, ... }
-Construct a theory of at least three sentences which uses all three predicates and at least three different constants.

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