query: an infinite monoid that is not free monoid and does not contain any free monoid
positive_passages.docid: 156459
positive_passages.text: infinite monoid H that is not a free monoid and contains a free monoid as a submonoid
negative_passages.docid: 35115
negative_passages.text: Questions on how to prove that a set of connectives is NOT functionally complete
negative_passages.docid: 66398
negative_passages.text: Union of a finite set and a countably infinite set is countably infinite
negative_passages.docid: 108533
negative_passages.text: Is there any formula of monadic second-order logic that is only satisfied by an infinite set?
negative_passages.docid: 3104
negative_passages.text: Prove that a group is infinite and nonabelian.
negative_passages.docid: 39129
negative_passages.text: Simplest Example of a Poset that is not a Lattice
negative_passages.docid: 119888
negative_passages.text: Is it possible to convert $\forall$ quantifiers to $\exists$ quantifiers without negation?
negative_passages.docid: 7536
negative_passages.text: Is there an idempotent element in a finite semigroup?
negative_passages.docid: 146560
negative_passages.text: Is there any uncountably infinite set that does not generate the reals?
negative_passages.docid: 6755
negative_passages.text: A finite, cancellative semigroup is a group
negative_passages.docid: 101453
negative_passages.text: Existence of a Boolean algebra with a unique ultrafilter in ZF
negative_passages.docid: 6478
negative_passages.text: Prove that for any infinite poset there is an infinite subset which is either linearly ordered or antichain.
negative_passages.docid: 68230
negative_passages.text: The cardinality of a countable union of sets with less than continuum cardinality
negative_passages.docid: 85799
negative_passages.text: Finding languages such that $L_{1} \subseteq L_{2} \subseteq L_{3}$ where $L_{1}, L_{3} \notin \mathbb{R}$, $L_{2} \in \mathbb{R}$
negative_passages.docid: 62208
negative_passages.text: If $A$ is a non-empty set, then $A \notin A$
negative_passages.docid: 77548
negative_passages.text: Given an arbitrary infinite set $S$, how to construct an injection $\mathbb{N} \to S$ with the Axiom of Choice?
negative_passages.docid: 140553
negative_passages.text: An ideal which is not finitely generated