A remark on Mahler’s compactness theorem

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

A Remark on Zoloterav’s Theorem

Let n ≥ 3 be an odd integer. For any integer a prime to n, define the permutation γ a,n of {1,. .. , (n − 1)/2} by γ a,n (x) = n − {ax} n if {ax} n ≥ (n + 1)/2, {ax} n if {ax} n ≤ (n − 1)/2, where {x} n denotes the least nonnegative residue of x modulo n. In this note, we show that the sign of γ a,n coincides with the Jacobi symbol a n if n ≡ 1 (mod 4), and 1 if n ≡ 3 (mod 4).

On Compactness Theorem

In this talk we investigate the compactness theorem (as a property) in non-classical logics. We focus on the following problems: (a) What kind of semantics make a logic having compactnesss theorem? (b) What is the relationship between the compactness theorem and the classical model existence theorem (CME)/model existence theorem?

A Remark on the Compactness for the Cahn-Hilliard Functional

In this note we prove compactness for the Cahn-Hilliard functional without assuming coercivity of the multi-well potential.

Remark on a Theorem of Lindström

In a recent paper LindstrSm [I] proves a theorem on finite sets and he also proves a transfinite extension. In this note we only concern ourselves with the transfinite case of Lindstriim’s theorem. He in fact proves the following theorem: Let / Y I = K be an infinite set, and let A,, l K, be subsets of Y. Then for every p -=z m there are p disj...