# Tagged Questions

**7**

votes

**1**answer

252 views

### The definition of < in Robinson's Q

I recently had to explain how the basic axioms in Simpson's Subsystems of Second Order Arithmetic were interpretable in Robinson's Q. Most of the axioms are actually the same, except that Simpson ...

**5**

votes

**1**answer

116 views

### Attribution of an equivalence of the existence of omega-models of RCA0

There are many well-known equivalences in reverse mathematics between statements of the form "Every set is contained a countable coded $\omega$-model of $T$" and $S$, where $S, T$ are subsystems of ...

**0**

votes

**0**answers

107 views

### What references cover finitary systems of Ramified Analysis with transfinite levels?

The ramified theory of types, invented by Bertrand Russell, is a way of dealing with impredicativity by breaking the comprehension schema of second-order logic into levels. The comprehension schema ...

**3**

votes

**1**answer

201 views

### Reverse mathematics, Ramsey theorem and mass problem

If we look at reverse mathematics statements as mass problems, considering the class of solutions of an instance, it is known that Weak König's lemma has a maximal instance in the sense that there is ...

**4**

votes

**1**answer

191 views

### Who first proved there's an $\omega$-model of $\mathsf{WKL}_0$ in which all sets are low?

I am trying to pin down: who first proved that $\mathsf{WKL}_0$ has an $\omega$-model in which every set is of low degree? As shown in Simpson's Subsystems of Second Order Arithmetic (Theorem ...

**9**

votes

**2**answers

392 views

### Reverse mathematics below RCA

I'm sure this is a fairly basic question, but I can't seem to find a solid answer:
My primary question is: Is there a reasonably nice subsystem of second-order arithmetic corresponding essentially to ...

**8**

votes

**5**answers

1k views

### Understanding the nature and structure of proofs; Reverse Mathematics and Proof Theory. Prerequisites? Good introductory texts?

I'm still studying maths at undergraduate level, but intend to continue exploring topics in pure maths after I have graduated, so am thinking already about what directions I'd like to persue now, (as ...