# Tagged Questions

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### Best algebra text for Model Theory

I'm looking for an algebra book that is tailored towards some of the ideas in Model Theory, I'm currently slogging through Hodges' Model Theory. I'm a bit rusty with my algebra and was curious if ...
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### real closure of an archimedean field

my question is: Is an archimedean field dense in its real closure? I know that in the non-archimedean case, this does not have to be true (e.g., rational fucntions). Thanks!
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### When a subgroup of automorphism group of a structure is in the form of automorphism group of a substructure?

Question 1: Is the following statement true? ($*$) Let $\mathcal{L}$ be a first order language and $\mathcal{M}$ a $\mathcal{L}$-structure and $H\leq Aut(\mathcal{M})$ then there exists a ...
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### Counter example of monotone union [duplicate]

I saw this exercise in "Elements of Abstract and Linear Algebra" by E. H. Connell: Suppose $G$ is a group. Suppose $T$ is an index set and for each $t \in T$, $H_t$ is a subgroup of $G$. Furthermore, ...
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### Putting down axioms for some symbols. Playing with their consequences qualitatively and symbolically. Building theories. The book?

I am interested in the design and building of theories. By building theories, I mean putting down axioms of various kinds, over various fields, exploring their perhaps interesting, or probably boring, ...
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### The composition of functors and algebraic structures

An algebraic structure can be viewed as a finite-product-preserving functor $X : \mathbf{L} \rightarrow \mathbf{C},$ where $\mathbf{L}$ is a Lawvere theory and $\mathbf{C}$ is a category. Thus given ...
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### Problem concerning formally real fields

I'm trying to reconcile a fact I am reading in David Marker's Model Theory text. He claims on page 326 that $\mathbb{F}=\mathbb{Q}(\sqrt{2}, \sqrt{-2})$ is a formally real field. This seems like it ...
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### Introduction to Valued Fields

I'm looking for an introductory text on valued fields, to be used as the basis for a reading group for model theorists. Currently, I know of one such text, Valued Fields by Engler/Prestel. However, ...
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### Prove $\forall r \in \mathbb{R}. \exists k \in \mathbb{Z}. r < k$

I would like to prove that for every real number there exists an integer that is greater than it. My problem lies in that I am not sure how to construct the real numbers and provide their theory with ...
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### Renaming the elements of a mathematical structure

One of the most basic insights about mathematical structures is that we can rename their elements without fundamentally changing the structure. Question. How do we actually formalize this observation ...
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### What is exactly the meaning of being isomorphic?

I know that the concept of being isomorphic depends on the category we are working in. So specifically when we are building a theory, like when we define the natural numbers, or the real numbers, or ...
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### Class of finite groups a Fraïssé Class? [duplicate]

Is the class of finite groups a Fraïssé class? Calling this class $K$, does $K$ satisfy the following: Joint embedding property Amalgamation property Hereditary property: if $G \in K$ and $H \le G$, ...
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### cardinality of elements in a “semiring minus multiplicative identity”

In a theory that has all axioms of semiring except multiplicative identity axiom, will there be a model of the theory that has infinite elements? The model must violate multiplicative identity axiom.
### how do we prove that ring of characteristic $p$ has arbitrarily large models?
As title says, how do we prove that the theory that describes ring of characteristic $p$ has arbitrarily large model? I am asking for a model-theoretic approach.