Garrett Ervin

activity

20162026

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4 papers · 1 filter

math.LO2023

Left absorption in products of countable orders

Garrett Ervin, Ethan Gu

We classify the countable linear orders $X$ for which there is an order $A$ with at least two points such that the lexicographic product $A X$ is isomorphic to $X$ . Given such an $X…

math.LO2023

Decomposing the real line into everywhere isomorphic suborders

Garrett Ervin

We show that if $R = A \cup B$ is a partition of $R$ into two suborders $A$ and $B$ , then there is an open interval $I$ such that $A \cap I$ is not order-isomorph…

math.LO2018

Distinct orders dividing each other on both sides

Garrett Ervin

We construct non-isomorphic linear orders X and Y that are both left-hand and right-hand divisors of one another, answering positively a question of Sierpinski.

math.LO2016

Every linear order isomorphic to its cube is isomorphic to its square

Garrett Ervin

In 1958, Sierpinski asked whether there exists a linear order $X$ that is isomorphic to its lexicographically ordered cube but is not isomorphic to its square. The main result of t…