PA* is finitely consistent (i.e., every finite subset of PA* is consistent) hence consistent, hence by the Completeness Theorem it has a model.
Why not every finite resource?
We resolve a 1983 question of Serre by constructing curves with many points of every genus over every finite field.
For every finite set a1, a2, …, ak of positive integers, there exists a largest integer that divides each of these numbers, called their greatest common divisor (GCD).
The minimax theorem, which von Neumann proved in 1928, states that every finite, two-person constant-sum game has a solution in pure or mixed strategies.
Because every finite group is made up of "composition factors"—building blocks that are finite simple groups theorems about simple groups have ramifications for all finite groups.
for every finite sequence,.
He concludes that every physical system implements every finite automaton.
If n = ℵ0, Łn is contained in every finite Łn.
Thus, every finite order meromorphic solution of (3) is rational.
Theorem 4.1 holds for every finite interval,,, and, when.
