When a linear order has an order preserving surjection onto each of its suborders, we say that it is strongly surjective. We prove that the set of countable strongly surjective linear orders is a Ď2(II11)-complete set. Using hypotheses beyond ZFC, we prove the existence of uncountable strongly surjective orders.
Linear orders: when embeddability and epimorphism agree
CAMERLO, RICCARDO;
2019-01-01
Abstract
When a linear order has an order preserving surjection onto each of its suborders, we say that it is strongly surjective. We prove that the set of countable strongly surjective linear orders is a Ď2(II11)-complete set. Using hypotheses beyond ZFC, we prove the existence of uncountable strongly surjective orders.
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