Liquid-crystalline mixture comprising at least one compound of the formula where the following applies to the symbols occurring: Y is O; Z 1 is a single bond; Z 2 is on each occurrence, identically or differently, a single bond or a group selected from O, S, -C(R 3) 2 -, -C(R 3) 2 O-, -OC(R 3) 2 -, -CR 3 =CR 3 - and -C≡C-, or two, three, four or five groups selected from the said groups combined with one another; Ar 1 is on each occurrence, identically or differently, an aryl or heteroaryl group having 5 to 30 aromatic ring atoms, which may be substituted by one or more radicals R 4; R 1 is on each occurrence, identically or differently, F or a straight-chain alkyl or alkoxy group having 3 to 12 C atoms, which may be substituted by one or more radicals R 5, or a branched alkyl or alkoxy group having 3 to 12 C atoms, which may be substituted by one or more radicals R 5, or a cyclic alkyl group having 6 C atoms, which may be substituted by one or more radicals R 5, where one or more CH 2 groups in the alkyl and alkoxy groups may be replaced by -O- or -S-. R Y, R 2, R 3, R 4 are on each occurrence, identically or differently, H, D, F, Cl, CN, N(R 5) 2, an alkyl, alkoxy or thioalkoxy group having 1 to 15 C atoms or an alkenyl or alkynyl group having 2 to 15 C atoms, where the above-mentioned groups may in each case be substituted by one or more radicals R 5 and where one or more CH 2 groups in the above-mentioned groups may be replaced by -R 5 C=CR 5 -, -C≡C-, C=O, C=S, -C(=O)O-, -O(C=O)-, Si(R 5) 2, NR 5, -O- or -S-, or an aryl or heteroaryl group having 5 to 30 aromatic ring atoms, which may in each case be substituted by one or more radicals R 5; R 5 is on each occurrence, identically or differently, H, D, F, Cl, CN, N(R 6) 2, an alkyl, alkoxy or thioalkoxy group having 1 to 15 C atoms or an alkenyl or alkynyl group having 2 to 15 C atoms, where the above-mentioned groups may in each case be substituted by one or more radicals R 6 and where one or more CH 2 groups in the above-mentioned groups may be replaced by -R 6 C=CR 6 -, -C≡C-, C=O, C=S, -C(=O)O-, -O(C=O)-, Si(R 6) 2, NR 6, -O- or -S-, or an aryl or heteroaryl group having 5 to 30 aromatic ring atoms, which may in each case be substituted by one or more radicals R 6; R 6 is on each occurrence, identically or differently, H, F or an aliphatic organic radical having 1 to 20 C atoms, in which one or more H atoms may be replaced by F, or an aryl or heteroaryl group having 5 to 20 C atoms, in which one or more H atoms may be replaced by F; i is on each occurrence, identically or differently, 0, 1, 2, 3 or 4; and at least one further compound selected from liquid-crystalline compounds, where the at least one compound of the formula is present in solution. Y is O; Z 1 is a single bond; Z 2 is on each occurrence, identically or differently, a single bond or a group selected from O, S, -C(R 3) 2 -, -C(R 3) 2 O-, -OC(R 3) 2 -, -CR 3 =CR 3 - and -C≡C-, or two, three, four or five groups selected from the said groups combined with one another; Ar 1 is on each occurrence, identically or differently, an aryl or heteroaryl group having 5 to 30 aromatic ring atoms, which may be substituted by one or more radicals R 4; R 1 is on each occurrence, identically or differently, F or a straight-chain alkyl or alkoxy group having 3 to 12 C atoms, which may be substituted by one or more radicals R 5, or a branched alkyl or alkoxy group having 3 to 12 C atoms, which may be substituted by one or more radicals R 5, or a cyclic alkyl group having 6 C atoms, which may be substituted by one or more radicals R 5, where one or more CH 2 groups in the alkyl and alkoxy groups may be replaced by -O- or -S-. R Y, R 2, R 3, R 4 are on each occurrence, identically or differently, H, D, F, Cl, CN, N(R 5) 2, an alkyl, alkoxy or thioalkoxy group having 1 to 15 C atoms or an alkenyl or alkynyl group having 2 to 15 C atoms, where the above-mentioned groups may in each case be substituted by one or more radicals R 5 and where one or more CH 2 groups in the above-mentioned groups may be replaced by -R 5 C=CR 5 -, -C≡C-, C=O, C=S, -C(=O)O-, -O(C=O)-, Si(R 5) 2, NR 5, -O- or -S-, or an aryl or heteroaryl group having 5 to 30 aromatic ring atoms, which may in each case be substituted by one or more radicals R 5; R 5 is on each occurrence, identically or differently, H, D, F, Cl, CN, N(R 6) 2, an alkyl, alkoxy or thioalkoxy group having 1 to 15 C atoms or an alkenyl or alkynyl group having 2 to 15 C atoms, where the above-mentioned groups may in each case be substituted by one or more radicals R 6 and where one or more CH 2 groups in the above-mentioned groups may be replaced by -R 6 C=CR 6 -, -C≡C-, C=O, C=S, -C(=O)O-, -O(C=O)-, Si(R 6) 2, NR 6, -O- or -S-, or an aryl or heteroaryl group having 5 to 30 aromatic ring atoms, which may in each case be substituted by one or more radicals R 6; R 6 is on each occurrence, identically or differently, H, F or an aliphatic organic radical having 1 to 20 C atoms, in which one or more H atoms may be replaced by F, or an aryl or heteroaryl group having 5 to 20 C atoms, in which one or more H atoms may be replaced by F; i is on each occurrence, identically or differently, 0, 1, 2, 3 or 4;