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Gödel's first

**incompleteness****theorem**states that all consistent axiomatic formulations of number theory which include Peano arithmetic include undecidable propositions ...A formal theory is said to be incomplete if it contains fewer theorems than would be possible while still retaining consistency.

Gödel's second

**incompleteness****theorem**states no consistent axiomatic system which includes Peano arithmetic can prove its own consistency. Stated more colloquially, any ...A

**theorem**is a statement that can be demonstrated to be true by accepted mathematical operations and arguments. In general, a**theorem**is an embodiment of some general ...The Paris-Harrington

**theorem**is a strengthening of the finite Ramsey's**theorem**by requiring that the homogeneous set be large enough so that cardH>=minH. Clearly, the ...The converse of Fisher's

**theorem**.There are several theorems that generally are known by the generic name "Pappus's

**Theorem**." They include Pappus's centroid**theorem**, the Pappus chain, Pappus's harmonic ...Qualitatively, a deep

**theorem**is a**theorem**whose proof is long, complicated, difficult, or appears to involve branches of mathematics which are not obviously related to the ...The reciprocity

**theorem**for x^8=q (mod p).There are so many theorems due to Fermat that the term "Fermat's theorem" is best avoided unless augmented by a description of which

**theorem**of Fermat is under discussion. ......