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Last seen on: –L.A. Times Daily Crossword – Aug 18 2022
NY Times Crossword 21 Nov 20, Saturday

Random information on the term “ELEMENTARY”:

In proof theory, a branch of mathematical logic, elementary function arithmetic (EFA), also called elementary arithmetic and exponential function arithmetic, is the system of arithmetic with the usual elementary properties of 0, 1, +, ×, xy, together with induction for formulas with bounded quantifiers.

EFA is a very weak logical system, whose proof theoretic ordinal is ω3, but still seems able to prove much of ordinary mathematics that can be stated in the language of first-order arithmetic.

EFA is a system in first order logic (with equality). Its language contains:

Bounded quantifiers are those of the form ∀(x<y) and ∃ (x<y) which are abbreviations for ∀ x (x<y)→… and ∃x (x<y)∧… in the usual way.

The axioms of EFA are

Harvey Friedman’s grand conjecture implies that many mathematical theorems, such as Fermat’s Last Theorem, can be proved in very weak systems such as EFA.

The original statement of the conjecture from Friedman (1999) is:

ELEMENTARY on Wikipedia