Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 158 / 2 / i

Table of contents
- Solution i

Solution

Let

T \subseteq (X \times ω)^{< ω}

be a Suslin representation of

A

, and let

f : X \to Y

be injective. Apply

f

coordinatewise to the first coordinate of every node and put

T_{f} = {(f \circ s, t) : (s, t) \in T} \subseteq (Y \times ω)^{< ω} .

The injectivity of

f

ensures that a sequence is a branch of

T_{f}

exactly when its first coordinate decodes to a branch of

T

. Hence

p [T_{f}] = p [T] = A

, proving that every X-Suslin set is

Y

-Suslin whenever

X

injects into

Y

.

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