About

Hi! I’m Michael Weiss.

This blog is mostly about math. A little bit of history. And some random stuff.

I hope you find something to enjoy.

2 responses to “About”

  1. Pablo Ibáñez's avatar Pablo Ibáñez
    May 29, 2024 at 5:41 pm

    Dear Mr Weiss.

    I have seen an answer from you at https://math.stackexchange.com/questions/4683244/what-would-happen-in-predicate-logic-if-the-domain-of-discourse-was-allowed-to-b

    Would you be so kind as to tell me where in Hodges’ book A Shorter Model Theory I can find the example you mention about the substructure ⟨Y⟩=∅?

    Best whises

    Reply
    • Michael Weiss's avatar Michael Weiss
      May 30, 2024 at 8:22 am

      Hodge doesn’t state this explicitly as far as I can tell, but it’s implicit in Lemma 1.2.2 (p.7). If Y is empty and the language has no constants, then ∅ satisfies the conditions for 〈∅〉B. It contains cB for every constant c (since there are no constants), and is closed under the functions, since there are no n-tuples to apply the functions to.

      Reply

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